With the growing interest in wireless sensor networks (WSNs), minimizing network delay and maximizing sensor (node) lifetime are important challenges. Since the sensor battery is one of the most precious resources in a WSN, efficient utilization of the energy to prolong the network lifetime has been the focus of much of the research on WSNs. For that reason, many previous research efforts have tried to achieve tradeoffs in terms of network delay and energy cost for such data aggregation tasks. Recently, duty-cycling technique, i.e., periodically switching ON and OFF communication and sensing capabilities, has been considered to significantly reduce the active time of sensor nodes and thus extend network lifetime. However, this technique causes challenges for data aggregation. In this paper, we present a distributed approach, named distributed delay efficient data aggregation scheduling (DEDAS-D) to solve the aggregation-scheduling problem in duty-cycled WSNs. The analysis indicates that our solution is a better approach to solve this problem. We conduct extensive simulations to corroborate our analysis and show that DEDAS-D outperforms other distributed schemes and achieves an asymptotic performance compared with centralized scheme in terms of data aggregation delay.